The United States National Oceanic and Atmospheric Administration (NOAA) has an excellent site: About Water Levels, Tides and Currents. Dean Pentcheff's WWW Tide and Currect Predictor gives today's tides for many locations. The NOAA gives One year predictions for a large number of U.S. sites. My main reference for this column has been Paul Schureman, Manual of Harmonic Analysis and Prediction of Tides, U.S. Department of Commerce, Coast and Geodetic Survey, Special Publication No. 98, U.S. Government Printing Office, Washington, 1958 (reprinted May 1988).
1. Ocean Tides
Tides in the Bay of Fundy: Hall's Harbour, Nova Scotia and Hall's Harbour, six hours later.
Images courtesy Nova Scotia Tourism Office.
Going into or out of a harbor, or anchoring near a shore, you need to know in advance about the behavior of the tide. Here is what happened to Julius Caesar when he first landed in Britain, in 55 B.C. In his own words:
The expedition was cut short by this disaster.
The tide is caused by the pull of the sun and the moon on the oceans, and the rotation of the earth, but its exact pattern at any particular spot on the coast depends on the shape of the coastline and on the profile of the sea floor nearby. So even though the forces that move the tide are completely understood, the tides at any one spot are essentially impossible to calculate theoretically. What we can do is record the height of the tide at that spot over a certain period of time, and use these measurements to predict the tides at that spot in the future.
This process is of mathematical interest, because the tidal record is not periodic.
The tidal force is governed by a small number of astronomical motions which are themselves periodic, but since the various frequencies have no whole-number ratios between them, the whole configuration never repeats itself exactly. Nevertheless, a geometric analysis of the problem shows that the tidal force can be expressed as a finite sum of periodic functions whose frequencies are known (they are in fact small integral linear combinations of the astronomical frequencies). Once this is established, Fourier analysis can be applied to the tidal record from any port using this finite number of frequencies as a basis.
Modern tidal analysis and prediction in all its mathematical and mechanical detail is due to Sir William Thomson (later Lord Kelvin), around 1867. The theory rests on earlier work by Laplace, Young and Airy.
This is the first of three columns on the subject. This one treats the geometric analysis mentioned above. Part II will cover the Fourier analysis of the tidal record. Part III will examine the problem of synthesis, and in particular the tidal predicting machines devised by Kelvin and his collaborators. These mechanisms, monuments of 19th-century ingenuity, were only relatively recently (1965) replaced by digital computers in preparing the official U.S. tide predictions.
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